Parity
Hmmm... what the heck is parity, and how does it apply to bridge?
Well, the definition of Parity is taken from both mathematics and computer science:
    A relation between a pair of integers:
    If both integers are odd or both are even they have the same     parity; If one is odd and the other is even then they have a different parity.  Quantities with an even number of integers have even parity, while those with an odd number of integers have odd parity.
We can apply the definition to bridge hands, too, where it's easier to understand... deal 13 cards of one suit to four hands, and one hand will hold an odd number in that suit while the other three will have an even number -- or -- one hand will hold an even number of cards, and the other three hands will each have an odd number.  Another way to think of it is that three suits will have the same parity, either even or odd.

How will that help in bridge?  If your partner can tell you somehow that he has an odd number of cards in a particular suit, and you see an odd number of them in the dummy, but you hold an even number, then declarer must have an odd number, because three hands must have the same parity.

The concept can be extended to the parity of the four suits as well...   A player will hold three suits each with an odd number in them, and one suit that has an even number in it, or three suits will be even in parity with one suit that is odd.

Roy Wilson - September, 2018      


Count Signals
It takes awhile after we first learn the game to start watching for partner's signals, and we have to know the difference between an attitude signal and a count signal, but if you are able to read your partner's count signals and know that she holds either an odd number or an even number in a particular suit, you can quickly deduce the parity of that suit and will know if declarer has an odd number or an even number in the same suit.  (Note:  Zero is considered an even number so a void is considered as even parity.)

Parity Ace - King Leads
The concept of leading either the ace or the king when holding both honors to show parity is not well known here in the United States, and doesn't really have a high acceptance in Europe either, but the idea has advocates in the Scandinavian countries and is worth your consideration.  Kibitz those teams on BBO, BridgeBaseOnline, and you will see them sometimes lead the ace and other times lead the king.  The choice depends on how many they have in the suit.
    Holding both the ace and king of a suit you wish to lead, choose the ace when you have an even number in the suit and choose the king with an odd number.
    Lead the A with the first hand, but lead the king with the second.

    You have even parity with both hands (Three suits are even in number) but your leads tells your partner the parity of the spade suit.  That's probably enough information, with the dummy and her own hand, to know declarer's distribution.




Two Examples of Using Parity on Defense
Parity Ace-King Opening Lead
Declarer is on your left and is in a 4 contract.
Your partner leads the K, showing an odd number in the suit.  You play the deuce, indicating an odd number, which might be one, three or five.  Declarer drops the Q and partner shifts to a "safe" club.  You can see you will be in as soon as declarer leads a trump, so what will you lead back to partner?  Was that Q a singleton? If so, you need to return a diamond before declarer dumps diamonds on the club suit.
    Look at the parity of the heart suit...
    Partner has an odd number, the dummy has an odd number, and you also have an odd number.
    Declarer must have an even number!  That Q was a false card.  Return a heart because declarer has a heart loser that would probably be pitched on the club suit.

Pseudo Squeeze
You hold this hand, sitting East.
    N O R T H
      A 2
      9 4
      T 8 7 6 2
      K J 6 3

      A 2
      9 4
      T 8 7 6 2
      K J 6 3


South is the dealer and opens with a 4 bid.  Everyone passes and your partner leads a trump, specifically the J.

Now you see the dummy...



Declarer takes the lead and plays eight more spades, nine total, then she plays the A and both the A and K.
That's 12 cards and you are down to your last two cards which are the K and the A - you have to discard one of them.
Declarer has one card left in the dummy, and it's the K.
Which card do you hold?


Trick Question?
Perhaps... I didn't tell you which cards your partner discarded, right?  Even so, this sort of thing happens often.  We all have found ourselves in this position, wishing we had paid more attention to the count and the discards.


Trick Question?
Perhaps... I didn't tell you which cards your partner discarded, right?  Even so, this sort of thing happens often.  We all have found ourselves in this position, wishing we had paid more attention to the count and the discards.



Would it help you if you knew your partner started with an odd number of hearts and an even number of clubs?  She had only a doubleton spade and discarded high-low in clubs.  She also played high-low when the top diamonds were cashed by declarer.  When she discarded hearts she started with the deuce.

Every hand you ever pick up will have three suits that are even in number and one suit that has an odd number, or three suits that are odd in number and one suit that has an even number.  That's the nature of 13 cards held in four hands.  The clue here is that you know partner has an odd number of hearts.  The dummy and you both hold an even number of hearts, which means that declarer must also hold an even number!  Only one player can have an odd number in a suit when the other three have an even number.  In this case, it's your partner.  Save your K --     Not the A ! !

Oh... and why is it called a Pseudo Squeeze?  Because you are not squeezed if you know the right card to keep.  In an actual squeeze you cannot keep a winner because there is no "right" card. Here's the full hand...